764edo: Difference between revisions

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== Theory ==

764edo is a very strong 17-limit system ~~distinctly~~ [[consistent]] to the 17-odd-limit, and is the fourteenth [[~~The Riemann zeta function and tuning #Zeta EDO lists|~~zeta integral edo]]. In the 5-limit it tempers out the hemithirds comma, {{monzo| 38 -2 -15 }}; in the 7-limit [[4375/4374]]; in the 11-limit [[3025/3024]] and [[9801/9800]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; and in the 17-limit [[2431/2430]], [[2500/2499]], [[4914/4913]] and [[5832/5831]]. It provides the [[optimal patent val]] for the [[abigail]] temperament in the 11-limit.

764edo is a very strong 17-limit system [[consistency|distinctly consistent]] to the [[17-odd-limit]], and is the fourteenth [[zeta integral edo]]. In the 5-limit it [[tempering out|tempers out]] the hemithirds comma, {{monzo| 38 -2 -15 }}; in the 7-limit [[4375/4374]]; in the 11-limit [[3025/3024]] and [[9801/9800]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; and in the 17-limit [[2431/2430]], [[2500/2499]], [[4914/4913]] and [[5832/5831]]. It provides the [[optimal patent val]] for the [[abigail]] temperament in the 11-limit.

In higher limits, it is a strong no-19 and no-29 37-limit tuning, and an exceptional 2.11.23.31.37 subgroup system, with errors less than 2%.

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=== Subsets and supersets ===

Since 764 factors into ~~2<sup>2</sup> × 191~~, 764edo has subset edos 2, 4, 191, and 382. In addition, one step of 764edo is exactly 22 [[jinn]]s.

Since 764 factors into {{factorization|764}}, 764edo has subset edos 2, 4, 191, and 382. In addition, one step of 764edo is exactly 22 [[jinn]]s ([[16808edo|22\16808]]).

== Regular temperament properties ==

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! Generator*

! Cents*

! Associated<br>Ratio

! Associated<br>Ratio*

! Temperaments

|-

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is a very strong 17-limit system distinctly [[consistent]] to the 17-odd-limit, and is the fourteenth [[The Riemann zeta function and tuning #Zeta EDO lists|zeta integral edo]]. In the 5-limit it tempers out the hemithirds comma, {{monzo| 38 -2 -15 }}; in the 7-limit [[4375/4374]]; in the 11-limit [[3025/3024]] and [[9801/9800]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; and in the 17-limit [[2431/2430]], [[2500/2499]], [[4914/4913]] and [[5832/5831]]. It provides the [[optimal patent val]] for the [[abigail]] temperament in the 11-limit.
+edo is a very strong 17-limit system [[consistency|distinctly consistent]] to the [[17-odd-limit]], and is the fourteenth [[zeta integral edo]]. In the 5-limit it [[tempering out|tempers out]] the hemithirds comma, {{monzo| 38 -2 -15 }}; in the 7-limit [[4375/4374]]; in the 11-limit [[3025/3024]] and [[9801/9800]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; and in the 17-limit [[2431/2430]], [[2500/2499]], [[4914/4913]] and [[5832/5831]]. It provides the [[optimal patent val]] for the [[abigail]] temperament in the 11-limit.
 In higher limits, it is a strong no-19 and no-29 37-limit tuning, and an exceptional 2.11.23.31.37 subgroup system, with errors less than 2%.
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 === Subsets and supersets ===
-Since 764 factors into 2<sup>2</sup> × 191, 764edo has subset edos 2, 4, 191, and 382. In addition, one step of 764edo is exactly 22 [[jinn]]s.
+Since 764 factors into {{factorization|764}}, 764edo has subset edos 2, 4, 191, and 382. In addition, one step of 764edo is exactly 22 [[jinn]]s ([[16808edo|22\16808]]).
 == Regular temperament properties ==
@@ Line 74: / Line 74: @@
 ! Generator*
 ! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperaments
 |-